I had great success with a slow progression on chin-ups. It was inspired by Selkow's Method and something I read here. (It might have been Selkow's method. It has been over a year.)
I found an amount of chin-ups I could do in one set. Then I subtracted 3-4 chins from that. I think I could do 7. My goal became to do 10 sets of 4.
I did 9 sets of 4 supersetted with upper body lifts. Then I did an AMRAP on the last set. Say I got 6. So my total for the day was 42.
The next week, I did 5 for two sets, then 4 for the rest and an AMRAP at the end. I divided that total up the same way. I gradually added reps to the earlier sets as dictated by my previous week's total. I ended up increasing my total by 2-3 most weeks and within the year was able to knock out 10x10.
I used different grips on the different days and thus different amounts of reps. On lower body days I went for weighted reps or inverted rows as needed. It isn't complicated but might seem like it. The bottom line is that I increased my total reps in small increments. Just like with anything, those small increases looked more significant after months.